Chapter 8: Implications for Everyday Systems

Section 7: Biological Pigmentation Patterns

Features of the [patterning] model

The model is a totalistic 2D cellular automaton, as discussed on page 927. It shows class 2 behavior in which information propagates only over limited distances, so that except when the total size of the system is comparable to the range of the rule, boundary conditions are not crucial.

Similar models have been considered before. In the early 1950s (see below) Alan Turing used a model which effectively differed mainly in having continuous color levels. In 1979 Nicholas Swindale constructed a model with discrete levels to investigate ocular dominance stripes in the brain (see below). And following my work on cellular automata in the early 1980s, David Young in 1984 considered a model even more similar to the one I use here.

There are simple cellular automata—such as 8-neighbor outer totalistic code 196623—which eventually yield maze-like patterns even when started from simple initial conditions. The rule on page 336 gives dappled patterns with progressively larger spots.

Image Source Notebooks:

From Stephen Wolfram: A New Kind of Science [citation]